Misc. 14 (Introduction)
If the matrix A is both symmetric and skew symmetric, then
A. A is a diagonal matrix
B. A is a zero matrix
C. A is a square matrix
D. None of these
Diagonal Matrix: Matrix with all non-diagonal elements zero.
Eg: [■8(1&0&0@0&−2&0@0&0&4)] , [■8(−9&0@0&35)]
Zero Matrix: Matrix with all elements zero
Eg: [■8(0&0&0@0&0&0@0&0&0)] , [■8(0&0@0&0)]
Square matrix
Matrix with number of rows = Number of columns
Eg: [■8(6&−2&2@−2&3&−1@2&−1&3)] , [■8(1&6@5&7)]
Misc. 14
If the matrix A is both symmetric and skew symmetric, then
A. A is a diagonal matrix
B. A is a zero matrix
C. A is a square matrix
D. None of these
Since A is both symmetric and skew-symmetric matrix,
A’ = A and A’ = –A
Comparing both equations
⇒ A = − A
⇒ A + A = O
⇒ 2A = O
⇒ A = O
Therefore, A is a zero matrix.